Answer:
x = 3
[tex] LM = 26 [/tex]
Step-by-step explanation:
Given:
[tex] LM = 8x + 2 [/tex]
[tex] MN = 10x - 4 [/tex]
Required:
Value of x and length of segment LM
SOLUTION:
Since M is the midpoint of line segment LN, it implies that:
[tex] LM = MN [/tex]
[tex] 8x + 2 = 10x - 4 [/tex] (substitution)
Combine like terms
[tex] 2 + 4 = 10x - 8x [/tex]
[tex] 6 = 2x [/tex]
Divide both sides by 2
[tex] \frac{6}{2} = \frac{2x}{2} [/tex]
[tex] 3 = x [/tex]
[tex] x = 3 [/tex]
[tex] LM = 8x + 2 [/tex]
Plug in the value of x
[tex] LM = 8(3) + 2 [/tex]
[tex] LM = 24 + 2 [/tex]
[tex] LM = 26 [/tex]
